I had an assignment and have to submit it after my holiday..hope you can solve it. ?

Question

1) 2(9^x) + 3^(x-1) + 4 = 2[3^(x +1)]

Find the first three terms of the expansion square root of (1 + 2x)/(1 - 2x )in ascending powers of x.

By substituting x = 0.01, find an approximation for square root of 51 correct to five significant figures.

Answer 1

1st QUESTION.

OK, two solutions are possible

1.) x = ln ( 3 / 2 ) / ln ( 3 ) = 0.36907

2.) x = ln ( 4 / 3 ) / ln ( 3 ) = 0.26186

To solve it simply write 9 = 3 ^ 2 and then divide the whole equation by 3 ^ x, it will give,

4 * (3 ^ -x) + 2 * (3 ^ x)  = 6 - 1/3

Now simplify (take the LCM which is 3^x on LHS) and write it as

6 * (3 ^ 2x) - 17 * (3 ^ x) + 12 = 0

Now take 3 ^ x = y, there fore, 3 ^ 2x will be  y ^ 2, it will now become a quadratic equation, 6 * (y ^ 2) - 17y + 12  = 0

Solve and then find the value of y = 3 ^ x, take ln on both sides and then calculate.

Good question.

To find the square root of 51 take B = sqrt (51)

Now use newton repitive error reduction method.

Answer 2

1) 2(9^x) + 3^(x-1) + 4 = 2[3^(x +1)]

x=0.369

This was solved by graphing and finding where the root lies (it lies between 0.3 and 0.4) and then using Newton's method.

You cannot solve it any other way.(i.e. algebraically)